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Stochastic Resonance in two Coupled Underdamped Bistable Systems.

Anatole Kenfack

We consider a system of two coupled underdamped oscillators driven by both periodic and noise sources. The phonemenon of stochastic resonance (SR), that is manisfest in nonlinear systems whereby a very weak signal can be amplified and optimized by the assistance of noise will be thoroughly insvestigated. This problem has been already considered in a similar coupled bistable systems but with the friction playing a major role~\cite{neiman1995}, i.e. the system is overdamped and thus predictible. In our system, chaos may show up and lead to interesting new phenomena. We plan to first provide a phase diagram as well as the bifurcation diagrams of the system. These digrams will provide us with the global view of our dynamical system and will certainly constitute a good guide as far as the choice of parameters in the follow-up will be concerned. We expect by suitably tuning both the coupling and the driving signal of our system, to numerically find a variety of interesting phenomena that may be undergone by the system, such as (i) the build-up (enhancement) and/or a destruction of the SR, (ii) the regime of perfect synchronization of the two oscillators, (iii) as well as chaotic domains.